# Higgs Field

Haelfix
Im a little confused about what the argument is exactly.

If you are saying that the RNG flow equations are fundamental, you won't get an argument out of me. The nature of these equations determines exactly when, where and what renormalization means (indeed what it means at a nonperturbative level).

Yes, sometimes these equations say: 'hi, im flowing to a nontrivial nongaussian fixed point' in which case all that means is you can't renormalize the theory perturbatively, but the theory isn't necessarily doomed as it could still make sense nonperturbatively.

All im saying is there are exactly solvable field theories that have been experimentally verified, whereby the renormalization procedure is perfectly well understood at a physical level. We know exactly what it means and we can *see* why we have to use it to match the nonperturbative *result*.

** Im a little confused about what the argument is exactly.
If you are saying that the RNG flow equations are fundamental, you won't get an argument out of me. **

They are *not* fundamental, they are merely a devise to probe (at some energy scale) the effective (physical) coupling constants of a theory given a finite lattice cutoff and some bare coupling constants. Under fundamental, I understand the objective bare´´ theory itself and not how we percieve it when we probe space at some characteristic length scale.

**The nature of these equations determines exactly when, where and what renormalization means (indeed what it means at a nonperturbative level). **

True, but not all information is given to you by UV fixpoints of the RNG flow AFAIK. In QED, the electron charge diverges at high energies (Landau pole), and becomes null in the IR limit : QED is perturbatively renormalizable but not nonperturbatively.

**
Yes, sometimes these equations say: 'hi, im flowing to a nontrivial nongaussian fixed point' in which case all that means is you can't renormalize the theory perturbatively, but the theory isn't necessarily doomed as it could still make sense nonperturbatively. **

True, and that amounts for example in the QFT approach to QG (and such nontrivial fixpoints are found already).

**
All I am saying is there are exactly solvable field theories that have been experimentally verified, whereby the renormalization procedure is perfectly well understood at a physical level. We know exactly what it means and we can *see* why we have to use it to match the nonperturbative *result*. **

True, the standard model is non-perturbatively renormalizable (thanks to the Higgs AFAIK - and the Landau pole of QED is dissolved). All I wanted to point out is that taking the continuum limit is (a) *not* a priori necessary (but the RNG flow still remains a useful toy obviously) (b) the ideas behind *renormalization* (and not necessarily RNG) and gauge symmetries are *not* adequate for unification in my opinion (as I explained) since it is in a clear sense an *a posteriori* fitting, it can never make *predictions* about *new building blocks* at higher energies *a priori* (by construction).

Furthermore, it does not provide me with any *physical* insight of the *details* of the scattering process (I agree that some understanding can be gained from regularizing feynman diagrams but that is by far not sufficient in my view). I did not get any comments to these thoughts (in which I am far from being alone btw). I agree with you that it works but NOT that it is a *necessary* cure, IMO the problem is to be found in the theory you start with in the first place or in the *procedure* of second quantization itself.

Cheers,

Careful

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Hi Haelfix,

Let me ask you a question (I will put aside the lack of Hilbert space representations in interacting QFT's) - others are also free to answer of course - : what possible conclusions would *you* reach if the Higgs were not to be found at *reasonable* energy scales (there is a limit to the argument : we have to look at higher energies´´ you know) ? For example: would it tell you something about (a) the a priori necessity of renormalization (b) the bare lagrangian you start with (c) second quantization (d) something even far more radical ?

Cheers,

Careful

Careful said:
Hi Ernie,
Your question : why does renormalization work ?´´can be seen from many points of view. The one I developped in the previous post (and I think was also Wilson's) basically boils down to the statement that taking the continuum limit should not be done in the first place. Given a certain cutoff and bare coupling constants which we fit to get the correct predictions, it seems plausible to think that any nonrenormalizable theory could be replaced by a renormalizable one on the effective scales we observe it given the fact that the effective coupling constants in front of the nonrenormalizable terms go to zero anyway in the IR limit.
Now, you might not like this fine tuning, but in the same way I do not like that the bare couplings go to infinity either. On the other hand, if you insist on taking the continuum limit, then it seems to me that you eliminate divergences due to the scattering of *pointlike* particles which is *elastic* at arbitrary high frequency modes. Now, for non renormalizable theories an infinite number of new interactions is necessary to achieve this (due to nonlinearities in the interactions which are non polynomial).
Cheers,
Careful
Thank you for taking so much trouble. I do take your points, though, like you, I am not entirely happy with them.
To be frank, some of the correspondents' attitudes remind me of that famous book where each contributor started with "There is only one correct interpretation of Quantum Theory..." but each gave a completely different version. (I cannot recall the title, but it was based on BBC radio broadcasts many years ago). You, I must congratulate on admitting and analysing the uncertainties. Thank you again. Since we are now unlikely to get any further, I shall bow out of the dispute.
cheers!
Ernie

Haelfix
I think we're talking past each other here.

WHen I say RNG is fundamental, I mean given some field theory (any field theory), it tells us something very concrete about the nature of the *real* result, eg the nonperturbative *thing* which is what we want afterall not just the series approximation.

Now as to which field theory ultimately is fundamental with regards to what nature is about, well Im not sure if we will ever find such a thing that is both the right answer as well as being manifestly correct at all energy scales. It could be entirely possible for instance, that QED is the last word on the subject. THe landau pole can be pushed up to very high energies, and we could maybe just say 'well the universe never goes to infinite energy, ergo qed is just what it is, despite a purely mathematical singularity'.

Ok, I don't happen to believe that, just like I don't believe QCD is the final word either (it is asymptotically free, and more or less perfectly valid naively at all energy scales) but its easy to just add more degrees of freedom (in fact you can always add more terms to any theory you can think off, losing gauge symmetry and renormalization makes this worse, not better).

So Why is 'gauge theory and renormalization fundamental?', I don't know but in the formers case it appears in every important physical case we know off. In the latters, well pretty much (with a few exceptions that I mentioned), these are the only instances of reasonably complex field theories where we can actually predict things (and they are also empirically hundreds of times more likely to appear in nature, for whatever reason than their nonrenormalizable counterparts).

Haelfix
As far as your other question. If we don't find the Higgs at say the LHC, I lose faith in SUSY first and foremost. And well, things become interesting.

There are some rather contrived models that have Higgs like scalar fields at much higher energies, but they tend to either introduce far too much finetuning, or they add so many new fields it just confuses me to death (and my belief in theories that I dont understand is identically zero)

Now, do I lose faith in the standard model and some of the theoretical underpinnings of field theory? Tough question, I would certainly think about it a little bit (i'd imagine everyone would sanity check themselves), its kinda hard to unlearn two decades of research that we've internalized. Fortunately I don't work in that field, so I'd imagine my job is intact if I merely speculate about some of the rather hard to belief alternatives out there.

Haelfix said:
Fortunately I don't work in that field, so I'd imagine my job is intact if I merely speculate about some of the rather hard to belief alternatives out there.
Me neither and I have never really payed too much attention to QFT (since it seems to me to be more fundamentally flawed). The only comment I have is when you say that renormalizable theories are more likely to appear in nature than nonrenormalizable ones. My point of view is that this does not matter too much (if we probe any theory at sufficiently small energies the nonrenormalizable terms are not important anyway) - and I do not want to take the continuum limit in the first place. You could argue against this and say that I must construct then a criterion which picks out my bare coupling constants and rules out all other terms I would add during renormalization but - in case you are only worried about constructing theories which fit observation - why care about it ?

Cheers,

Careful

Haelfix said:
As far as your other question. If we don't find the Higgs at say the LHC, I lose faith in SUSY first and foremost. And well, things become interesting.

Now, do I lose faith in the standard model and some of the theoretical underpinnings of field theory? Tough question, I would certainly think about it a little bit (i'd imagine everyone would sanity check themselves), its kinda hard to unlearn two decades of research that we've internalized. Fortunately I don't work in that field, so I'd imagine my job is intact if I merely speculate about some of the rather hard to belief alternatives out there.

You have my sympathy,Haelfix. I have had to unlearn a lot of physics twice, so a third time wouldn't be too hard----- and I think it inevitable in the next decade. May I might live to see it!

cheers

Ernie

I did not mean to cause this, I do not have the luxury to participate in this as I would like.

Bottom line is, dealing with the 'renormaliztion group' it is just a way of re-calibrating your search, that was so aptly said above ^^, and in this case the Higgs. You cannot fudge the factor in or it will not go unnoticed in the physics community.

Yes, to the reply dealing with our degrees and professors, I was also fortunate to have many professors that would tell us the same, 'stay of the box' or do not be afraid to create a workable mathematical approach to a problem.

Please excuse me on this generalization statement dealing with wonderful teachers and mentors. Well, most of them?

I just hope that data will give us the missing piece of the puzzle dealing with the Standard Model.

There was one statement about looking for the Higgs that caught my eye. Yes, but 50 years ago we did not have the LHC coming on line.

Happy New Year,
y

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